Feedback Polynomial Filtering and Control of Non-Gaussian Linear Time-Varying Systems

This paper deals with the optimal filtering and optimal output-feedback controlof discrete-time, linear time-varying non-Gaussian systems. In the hypothesisthat the time-varying and non-Gaussian distributions of the state and mea-surement noises have bounded and known moments up to a given order, thiswork extends previous results about polynomial filtering and optimal controlto the time-varying case. The properties of the resulting filtering and controlalgorithms are discussed in the light of a stable recursive representation of theKronecker powers of the system obtained through a suitable rewriting of thesystem with an output injection term. The resulting sub-optimal algorithm in-herits the structure and the properties of the classical LQG approach but withenhanced performance.